Sqrt (1+sin x) / cos x = 1

√ (1+sinx) / cosx=1

√ (1+sinx) = cosx ОДЗ: cosx≠0 x≠π/2+πn

1+sinx=cosx

sin² (x/2) + cos² (x/2) + 2*sin (x/2) * cos (x/2) - cos² (x/2) + sin² (x/2) = 0

2sin² (x/2) + 2sin (x/2) * cos (x/2) = 0

2*sin (x/2) * (sin (x/2) + cos (x/2)) = 0

sin (x/2) = 0

x/2=πn

x₁=2πn

sin (x/2) + cos (x/2) = 0

sin (x/2) = - cos (x/2) cos (x/2) ≠-1 x/2≠-π/2+2πn x≠π+2πn

tg (x/2) = - 1

x/2=-π/4+πn

x₂=-π/2+2πn x₂∉ по ОДЗ

Ответ: x₁=2πn.